The least natural number 'n' for which `(n-2)x^2+8x+n+4>sin^(-1)(sin12)+cos^(-1)(cos12) AA x in R` is

The least value of k for which (k-2)x^(2)+8x+k+4gtsin^(-1)(sin12)+cos^(-1)(cos12) for all x in R is

The least value of n for which (n -2) x^(2) + 8 x + n + 4 gt sin^(-1) ( sin 12) + cos^-1)( cos 12),AA x in R", where " n in N , is ..............

The least integral value of k for which (k-2)x^(2)+8x+k+4 gt Sin^(-1)(sin12)+Cos^(-1)(cos12) for all x in R , is

Let n be the smallest natural number for which the limit lim_(x rarr0)(sin^(n)x)/(cos^(2)x(1-cos x)^(3)) exists,then tan ^(-1)(tan n) is equal to

sin(n+1)xsin(n+2)x+cos(n+1)xcos(n+2)x=cosx

sin(n+1)xsin(n+2)x+cos(n+1)xcos(n+2)x=cosx

The least value of n in N for which (n - 4)x^(2) + 8x + n + 2 gt 0 AA x in R , is

Let n be a natural number such that n gt 4 and U_(n) =sin ^(n) x+ cos ^(n)x. Then which of the following is correct ?

sin (n +1) x sin (n +2) x + cos (n +1) x cos (n +2) x = cos x